Feldman (3-3) baffled his former Rangers teammates on two hits, issuing only one walk while striking out three in the 104-pitch gem.
Rizzo delivered a two-run single to cap a five-run fourth inning that broke the game open and added a two-run homer in the eighth as the Cubs took the makeup game of an April 17 rain-out.
Rangers starter Nick Tepesch (2-3) was lit up for six runs (five earned) on six hits over four full frames.
Former Cub Geovany Soto went 2-for-4 with an RBI for Texas.
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